13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- Figure 12. KTH data plotted respectively against area and CH, R [12] Figure 13. Threshold KTH for SAE52100 expressed in terms of area and CH, R [12] Particularly for very small distances, r, from the crack tip along the axis of symmetry, Eq. (5) yields r K π2 I yy (6) Where, KI = σ0 aπ is the stress intensity factor. Figure 14 shows an example of the comparison of stress field ahead of the tip of two different sizes of cracks under a stress intensity factor KI of 10 MPa m which were obtained by Eq. (5). In both cases, σ0 was determined so that KI is equal to 10 MPa m. In the large crack (e.g. 2a = 20 mm), the singular stress field decays very fast from the crack tip. In this case, Eq. (5) can be well represented by Eq. (6) to characterize the stress field near the crack tip. On the other hand, in the small crack (e.g. 2a = 0.02 mm), a large discrepancy arises between the stress fields in these two cracks. Such a discrepancy in the stress field near crack tip between small crack and large crack also arises even if the material is not the perfectly elastic but the elastic-plastic. For this reason, the tensile stress field ahead of the tip of small crack cannot be determined uniquely through the stress intensity factor alone, and therefore the calculated threshold values for small cracks show a crack size dependence. 3.3.2. Specimens having artificial surface defects For a planar cracks with arbitrary shape at specimen surface (cf. Fig. 11(b)), KImax along the crack front can be approximated by [7, 8, 10]. (a) KTH as a function of (m) 0 2 4 6 8 10 0 10 20 30 40 SAE52100 HV= 712 (b) KTH as a function of CH, R CH, R (ppm) 0 2 4 6 8 10 0 1 2 3 4 5 SAE52100 HV= 712 (a) KTH + 0.494 CH, R (MPa ) (m) 0 2 4 6 8 10 0 10 20 30 40 3.64 3.00 3.79 3.05 3.08 2.95 3.26 3.89 3.17 2.32 2.69 3.06 3.29 2.46 KTH + 0.494 CH, R = 3.89 + 0.0555 √area 3.03 (0.54) SAE52100, HV= 712 Number associated with each plot shows hydrogen content CH,R in mass ppm. ○ Non-metallic inclusion in smooth specimen ● Non-metallic inclusion in specimen having artificial defect ■ Estimated threshold value for the artificial surface defect (b) CH, R (ppm) KTH ‒ 0.0555 (MPa ) 0 2 4 6 8 10 0 1 2 3 4 5 SAE52100, HV= 712 Number associated with each plot shows hydrogen content CH,R in mass ppm. 2.32 2.69 3.05 3.06 3.89 3.79 3.64 3.00 2.46 2.95 3.17 3.26 3.29 3.08 KTH ‒ 0.0555 √area = 3.89 ‒ 0.494 CH, R 3.03 (0.54) ○ Non-metallic inclusion in smooth specimen ● Non-metallic inclusion in specimen having artificial defect ■ Estimated threshold value for the artificial surface defect
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